Continuation-Performance Decomposition in Dynamic Games with Irreversible Failure
Nicholas H. Kirk
TL;DR
The paper tackles dynamic games with irreversible failure, where failure terminates the continuation domain and traditional scalar evaluations become ill-posed. It develops the continuation–performance decomposition (CPD), proving that any intrinsic evaluation under failure must separate continuation from performance in a lexicographic order, with continuation prioritized by the continuation profile $C(oldsymbol{0sigma})$ and conditional performance captured by $ ilde{U}_i(oldsymbol{0sigma})$. A decoupling theorem shows CPD arises as the intrinsic representation limit when failure penalties become large, and the analysis yields a bank-run interpretation where viability vetoes can rationally drive collapse rather than purely coordination failures. The framework provides equilibrium admissibility criteria, clarifies information sensitivity near viability boundaries, and connects to a large-penalty payoff game equivalence, offering a representational solution to evaluating strategies in environments with absorbing failure. Overall, CPD preserves standard utility maximization on survival paths while formalizing why unconditional scalar aggregation is inappropriate when continuation domains differ, with broad implications for economic dynamics under irreversible events.
Abstract
Once failure is irreversible, continuation payoffs cannot be meaningfully aggregated across strategies that differ in their survival properties. Standard scalar evaluation sidesteps this by arbitrarily completing payoffs beyond termination, but such completions are extrinsic to the game form. This paper introduces continuation-performance decomposition (CPD), proving that any evaluation satisfying natural regularity conditions, such as failure-completion invariance, survival locality, and local expected-utility coherence -- must separate continuation from performance lexicographically. Continuation priority thus emerges as a consequence of well-posed evaluation, not as a behavioral assumption. We establish equivalence between CPD and the limit of games with diverging failure penalties, show that viability is a game-form invariant independent of payoffs, and apply the framework to bank runs: preemptive withdrawals reflect rational viability vetoes rather than coordination failure when continuation is distributively asymmetric. CPD resolves a representational problem, not a preference problem.